Fundamentals of Acoustics E-Book

Michel Bruneau

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch
• Veröffentlichungsjahr: 2013

Seitenzahl: 588

Beschreibung

The central theme of the chapters is acoustic propagation in fluid media, dissipative or non-dissipative, homogeneous or nonhomogeneous, infinite or limited, placing particular emphasis on the theoretical formulation of the problems considered.

Leseprobe

Table of Contents

Preface

Chapter 1. Equations of Motion in Non-dissipative Fluid

1.1. Introduction

1.2. Fundamental laws of propagation in non-dissipative fluids

1.3. Equation of acoustic propagation

1.4. Density of energy and energy flow, energy conservation law

Chapter 1: Appendix. Some General Comments on Thermodynamics

A.1. Thermodynamic equilibrium and equation of state

A.2. Digression on functions of multiple variables (study case of two variables)

Chapter 2. Equations of Motion in Dissipative Fluid

2.1. Introduction

2.2. Propagation in viscous fluid: Navier-Stokes equation

2.3. Heat propagation: Fourier equation

2.4. Molecular thermal relaxation

2.5. Problems of linear acoustics in dissipative fluid at rest

Chapter 2: Appendix. Equations of Continuity and Equations at the Thermomechanic Discontinuities in Continuous Media

A.1. Introduction

A.2. Equations of continuity

A.3. Equations at discontinuities in mechanics

A.4. Examples of application of the equations at discontinuities in mechanics: interface conditions

Chapter 3. Problems of Acoustics in Dissipative Fluids

3.1. Introduction

3.2. Reflection of a harmonic wave from a rigid plane

3.3. Spherical wave in infinite space: Green’s function

3.4. Digression on two- and one-dimensional Green’s functions in non-dissipative fluids

3.5. Acoustic field in “small cavities” in harmonic regime

3.6. Harmonic motion of a fluid layer between a vibrating membrane and a rigid plate, application to the capillary slit

3.7. Harmonic plane wave propagation in cylindrical tubes: propagation constants in “large” and “capillary” tubes

3.8. Guided plane wave in dissipative fluid

3.9. Cylindrical waveguide, system of distributed constants

3.10. Introduction to the thermoacoustic engines (on the use of phenomena occurring in thermal boundary layers)

3.11. Introduction to acoustic gyrometry (on the use of the phenomena occurring in viscous boundary layers)

Chapter 4. Basic Solutions to the Equations of Linear Propagation in Cartesian Coordinates

4.1. Introduction

4.2. General solutions to the wave equation

4.3. Reflection of acoustic waves on a locally reacting surface

4.4. Reflection and transmission at the interface between two different fluids

4.5. Harmonic waves propagation in an infinite waveguide with rectangular cross-section

4.6. Problems of discontinuity in waveguides

4.7. Propagation in horns in non-dissipative fluids

Chapter 4: Appendix. Eigenvalue Problems, Hilbert Space

A.1. Eigenvalue problems

A.2. Hilbert space

Chapter 5. Basic Solutions to the Equations of Linear Propagation in Cylindrical and Spherical Coordinates

5.1. Basic solutions to the equations of linear propagation in cylindrical coordinates

5.2. Basic solutions to the equations of linear propagation in spherical coordinates

Chapter 6. Integral Formalism in Linear Acoustics

6.1. Considered problems

6.2. Integral formalism of boundary problems in linear acoustics

6.3. Examples of application

Chapter 7. Diffusion, Diffraction and Geometrical Approximation

7.1. Acoustic diffusion: examples

7.2. Acoustic diffraction by a screen

7.3. Acoustic propagation in non-homogeneous and non-dissipative media in motion, varying “slowly” in time and space: geometric approximation

Chapter 8. Introduction to Sound Radiation and Transparency of Walls

8.1. Waves in membranes and plates

8.2. Governing equation for thin, plane, homogeneous and isotropic plate in transverse motion

8.3. Transparency of infinite thin, homogeneous and isotropic walls

8.4. Transparency of finite thin, plane and homogeneous walls: modal theory

8.5. Transparency of infinite thick, homogeneous and isotropic plates

8.6. Complements in vibro-acoustics: the Statistical Energy Analysis (SEA) method

Chapter 9. Acoustics in Closed Spaces

9.1. Introduction

9.2. Physics of acoustics in closed spaces: modal theory

9.3. Problems with high modal density: statistically quasi-uniform acoustic fields

9.4. Statistical analysis of diffused fields

9.5. Brief history of room acoustics

Chapter 10. Introduction to Non-linear Acoustics, Acoustics in Uniform Flow, and Aero-acoustics

10.1. Introduction to non-linear acoustics in fluids initially at rest

10.2. Introduction to acoustics in fluids in subsonic uniform flows

10.3. Introduction to aero-acoustics

Chapter 11. Methods in Electro-acoustics

11.1. Introduction

11.2. The different types of conversion

11.3. The linear mechanical systems with localized constants

11.4. Linear acoustic systems with localized and distributed constants

11.5. Examples of application to electro-acoustic transducers

Chapter 11: Appendix

A.1. Reminder about linear electrical circuits with localized constants

A.2. Generalization of the coupling equations

Bibliography

Index

First published in France in 1998 by Editions Hermès entitled “Manuel d’acoustique fondamentale”

First published in Great Britain and the United States in 2006 by ISTE Ltd

Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address:

ISTE Ltd6 Fitzroy SquareLondon W1T 5DXUKISTE USA4308 Patrice RoadNewport Beach, CA 92663USAwww.iste.co.uk 

© ISTE Ltd, 2006

© Editions Hermès, 1998

The rights of Michel Bruneau and Thomas Scelo to be identified as the authors of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act 1988.

Library of Congress Cataloging-in-Publication Data

Bruneau, Michel.

[Manuel d’acoustique fondamentale. English]

Fundamentals of acoustics / Michel Bruneau; Thomas Scelo, translator and contributor.

p. cm.

Includes index.

ISBN-13: 978-1-905209-25-5

ISBN-10: 1-905209-25-8

1. Sound. 2. Fluids--Acoustic properties. 3. Sound--Transmission. I. Title.

QC225.15.B78 2006

534--dc22

2006014582

British Library Cataloguing-in-Publication Data

A CIP record for this book is available from the British Library

ISBN 10: 1-905209-25-8

ISBN 13: 978-1-905209-25-5

Preface

The need for an English edition of these lectures has provided the original author, Michel Bruneau, with the opportunity to complete the text with the contribution of the translator, Thomas Scelo.

This book is intended for researchers, engineers, and, more generally, postgraduate readers in any subject pertaining to “physics” in the wider sense of the term. It aims to provide the basic knowledge necessary to study scientific and technical literature in the field of acoustics, while at the same time presenting the wider applications of interest in acoustic engineering. The design of the book is such that it should be reasonably easy to understand without the need to refer to other works. On the whole, the contents are restricted to acoustics in fluid media, and the methods presented are mainly of an analytical nature. Nevertheless, some other topics are developed succinctly, one example being that whereas numerical methods for resolution of integral equations and propagation in condensed matter are not covered, integral equations (and some associated complex but limiting expressions), notions of stress and strain, and propagation in thick solid walls are discussed briefly, which should prove to be a considerable help for the study of those fields not covered extensively in this book.

The main theme of the 11 chapters of the book is acoustic propagation in fluid media, dissipative or non-dissipative, homogeneous or non-homogeneous, infinite or limited, etc., the emphasis being on the “theoretical” formulation of problems treated, rather than on their practical aspects. From the very first chapter, the basic equations are presented in a general manner as they take into account the non-linearities related to amplitudes and media, the mean-flow effects of the fluid and its inhomogeneities. However, the presentation is such that the factors that translate these effects are not developed in detail at the beginning of the book, thus allowing the reader to continue without being hindered by the need for in-depth understanding of all these factors from the outset. Thus, with the exception ofChapter 10 which is given over to this problem and a few specific sections (diffusion on inhomogeneities, slowly varying media) to be found elsewhere in the book, developments are mainly concerned with linear problems, in homogeneous media which are initially at rest and most often dissipative.

These dissipative effects of the fluid, and more generally the effects related to viscosity, thermal conduction and molecular relaxation, are introduced in the fundamental equations of movement, the equations of propagation and the boundary conditions, starting in the second chapter, which is addressed entirely to this question. The richness and complexity of the phenomena resulting from the taking into account of these factors are illustrated in Chapter 3, in the form of 13 related “exercises”, all of which are concerned with the fundamental problems of acoustics. The text goes into greater depth than merely discussing the dissipative effects on acoustic pressure; it continues on to shear and entropic waves coupled with acoustic movement by viscosity and thermal conduction, and, more particularly, on the use that can be made of phenomena that develop in the associated boundary layers in the fields of thermoacoustics, acoustic gyrometry, guided waves and acoustic cavities, etc.

Following these three chapters there is coverage (Chapters 4 and 5) of fundamental solutions for differential equation systems for linear acoustics in homogenous dissipative fluid at rest: classic problems are both presented and solved in the three basic coordinate systems (Cartesian, cylindrical and spherical). At the end of Chapter 4, there is a digression on boundary-value problems, which are widely used in solving problems of acoustics in closed or unlimited domain.

The presentation continues (Chapter 6) with the integral formulation of problems of linear acoustics, a major part of which is devoted to the Green’s function (previously introduced in Chapters 3 and 5). Thus, Chapter 6 constitutes a turning point in the book insofar as the end of this chapter and through Chapters 7 to 9, this formulation is extensively used to present several important classic acoustics problems, namely: radiation, resonators, diffusion, diffraction, geometrical approximation (rays theory), transmission loss and structural/acoustic coupling, and closed domains (cavities and rooms).

Chapter 10 aims to provide the reader with a greater understanding of notions that are included in the basic equations presented in Chapters 1 and 2, those which concern non-linear acoustics, fluid with mean flow and aero-acoustics, and can therefore be studied directly after the first two chapters.

Finally, the last chapter is given over to modeling of the strong coupling in acoustics, emphasizing the coupling between electro-acoustic transducers and the acoustic field in their vicinity, as an application of part of the results presented earlier in the book.